Ah, the joy of decision time.
Everyone has a carpeted box. Screw that. Raw MDF or paint FTW. I leave all mine raw with the pencil marks still on it. Show off my scribbles I say.
Last box I built for myself, I had some Krylon enamel mixed to match my car. 10 coats of it, then 4 days to cure. Followed by 5 coats of PPG clear sprayed on. The paint looked 5 inches thick, still wet, and the brush marks in the blue looked so sexy.
Whatever you decide, make sure your box is fully sealed from moisture, as MDF will ruin fast if you have a minor leak. I say spray inside and out with Thompson's if you decide to carpet it.